For some early very related classifications (ordered chronologically) see
"The classification of simplicial 3-spheres with nine vertices into polytopes and nonpolytopes" ByNeighborly 4-polytopes with 9 vertices Altshuler, Bokowski and Steinberg - J Comb Theory, Series A, Steinberg1973
Neighborly 4-polytopesAn enumeration of combinatorial 3-manifolds with nine vertices Altshuler and neighborly combinatorial 3-manifolds with ten verticesSteinberg, ByDiscrete Math, 1976
Neighborly 4-polytopes and neighborly combinatorial 3-manifolds with ten vertices, Altshuler, Canad J MathCanad J Math 1977
Neighborly 4-polytopes with 9 vertices A AltshulerThe classification of simplicial 3-spheres with nine vertices into polytopes and nonpolytopes, L Altshuler, Bokowski and Steinberg - Journal of Combinatorial Theory, Series A Discrete Math, 19731980
Enumeration of 3-manifolds with 9 verticesThe complete enumeration of the 4-polytopes and 3-spheres with eight vertices, Altshuler and Steinberg, Pacific J Math, 1985
Neighborly 2-manifolds with 12 vertices A AltshulerAltshuler, J Bokowski, P Schuchert - journal of combinatorial theory, …, 1996
The complete enumeration of the 4-polytopes and 3-spheres with eight vertices
A AltshulerSchuchert, L Steinberg - Pacific journal of mathematicsJ Comb Theory, Series A, 19851996